The diode is used in parallel with the switch to act as a half wave rectifier as part of the low voltage DC power supply for the electronic doorbell. These are used in electronic doorbell chimes that can be wired into traditional 24 VAC doorbell circuits.

Pressing the doorbell button applies the full 24 VAC through the circuit which is detected by the chime and plays the melody. The low voltage DC supply allows the chime to continue even after the button is released.

They are directional, and need to be installed in the direction indicated by the chime mfg. If you don't have the info, you can usually try it one way, and if it doesn't continue to play after releasing the button, turn it around.

Just to clarify, but I think you know, the direction of the diode is relative to the two wires - not the switch itself.

As far as the nicks in the wires, electrically, they don't really pose a safety issue but could cause nuisance "ringing" if they touched. More of a concern to me would be that if the actual conductors are exposed enough, they could oxidize/corrode and lead to failure (breakage) of the wire conductor. Rather than tape, I'd recommend heat-shrink tubing over the individual wires.